Economics: How could a marginal analysis be helpful when deciding whether you should go to sleep or continue to study?

A marginal analysis would help you take a decision between the two alternatives.

In a marginal analysis, you would calculate or estimate, how much benefit you would get for an additional hour of study, and how much benefit you would get for an additional hour of seelp.

Depending on whether the additional hour or sleep or study gives you the most benefit, the decision is taken.